Finite Group Databasebeta

← #11865868

Subgroups — #11865868

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×#63932C211yesmaximal, characteristic, complemented
4#10593969C211yesmaximal, characteristic, complemented
5#10592715C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7#10591489C211yesmaximal, characteristic, complemented
8#10591481C211yesmaximal, characteristic, complemented
9#10590609C211yesmaximal, characteristic, complemented
10#10590607C211yesmaximal, characteristic, complemented
11#10590559C211yesmaximal, characteristic, complemented
12#10590547C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590336C211yesmaximal, characteristic, complemented
16#82307—31nomaximal
17#80534—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C2×#3799C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25#64084C2211yescharacteristic, complemented
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×C4×#67—21no—
30C3×#893C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#67⋊C4—21no—
33C3×D3×C22⋊C4—21no—
34C3×#875C2211yescharacteristic, complemented
35C3×C4×D12C2211yescharacteristic
36C3×C42×D3C2211yescharacteristic
37#63934—24no—
38#63932—24no—
39#63911C2211yescharacteristic, complemented
40#63906—21no—
41#63906—21no—
42#63880—21no—
43#63880—21no—
44#63866C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51#63637C2211yescharacteristic, complemented
52#63636C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×C4×D4—31no—
64C2×#932—31no—
65C2×#932—31no—
66C2×#914—31no—
67C2×#911—31no—
68#5668—31no—
69C4×D3×D4D311yescharacteristic, complemented
70#5477—31no—
71C3×#463—31no—
72#5162—31no—
73#5150—31no—
74#5057—31no—
75#5019—31no—
76#5019—31no—
77#5016—31no—
78#5016—31no—
79#5016—31no—
80#5016—31no—
81#5016—61no—
82#5016D311yescharacteristic, complemented
83#5015—31no—
84#5015—31no—
85#4966—31no—
86#4966—31no—
87#4924—31no—
88#4844—31no—
89#4837—31no—
90#4818—31no—
91#4803—31no—
92#4786—31no—
93#4771—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4D414yescomplemented
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—44no—
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3D411yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119#3799—22no—
120#3799—22no—
121#3795—22no—
122#3795—22no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C32×C42C2311yescharacteristic
126#3754—22no—
127#3753—22no—
128#3752—21no—
129#3752—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#214—22no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3D411yescharacteristic
142C3×C4×Dic3D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3—21no—
148#3716—22no—
149#3715—22no—
150#3714—22no—
151#3713—22no—
152#3711—22no—
153#3711—22no—
154#3036—91noSylow
155C22×C3×D4—31no—
156C23×C3×C4—61no—
157C2×#239—31no—
158C2×#237—31no—
159C2×D3×D4C2×D311yescharacteristic
160C2×#235—31no—
161C2×#235—31no—
162C22×C4×D3—21no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C3×#124—31no—
166C3×C4×D4—21no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—61no—
171C3×C4×D4—61no—
172C3×C4×D4C2×D311yescharacteristic
173C3×C4×D4C2×D311yescharacteristic
174C2×C3×C4⋊C4—31no—
175C2×C3×C22⋊C4—61no—
176C2×C3×C42—31no—
177#944—31no—
178C2×#215—31no—
179#940—31no—
180D4×Dic3C2×D311yescharacteristic
181C2×#214—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186C2×#214C2×D311yescharacteristic
187#932—64no—
188#932—64no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—61no—
195C2×#213C2×D311yescharacteristic
196#930—61no—
197#930—61no—
198C4×#67—21no—
199C2×#208—31no—
200C2×#208—31no—
201#914—64no—
202#911—64no—
203C2×D24—31no—
204C2×#204—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—31no—
207#893C2×D311yescharacteristic
208D3×C4⋊C4C2×D311yescharacteristic
209#884—61no—
210#884—61no—
211#67⋊C4—21no—
212#67⋊C4—61no—
213#67⋊C4—61no—
214D3×C22⋊C4—21no—
215#875—31no—
216#875—31no—
217#875—61no—
218#875C2×D311yescharacteristic, complemented
219#874—31no—
220C4×D12—61no—
221C4×D12—61no—
222C4×D12C2×D311yescharacteristic
223C42×D3C2×D311yescharacteristic
224#869—31no—
225C3×C4⋊C8—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#832—31no—
230#821—31no—
231#816—31no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234#810—31no—
235#810—31no—
236#810—31no—
237#810—31no—
238#810—61no—
239#810C2×D311yescharacteristic, complemented
240#809—31no—
241#809—31no—
242#809—31no—
243#809—31no—
244#809—61no—
245#809C2×D311yescharacteristic, complemented
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—61no—
251C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C32×D4—21no—
261C32×D4C2×D412yes—
262C2×C32×C4—21no—
263C2×C32×C4—42no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270#634—21no—
271#634—21no—
272C3×#67—24no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—42no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12C2×D412yes—
283C3×C4×D3—22no—
284C3×C4×D3—41no—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×C4×D3C2×D412yes—
289C3×C4×D3#4112yes—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#626—42no—
293#626—42no—
294#626—42no—
295#625—42no—
296#624—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C2×AGL(1,ℤ/8)—91no—
304#532—91no—
305C2×C4×D4—31no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#461—91no—
311#461—91no—
312#459—91no—
313#459—91no—
314#423—91no—
315#417—91no—
316#417—91no—
317C24×C3—61no—
318C23×D3—21no—
319C2×C3×Q8—31no—
320C2×C3×D4—21no—
321C2×C3×D4—34no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—62no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—41no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—124no—
339C2×#67—21no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—21no—
346C22×Dic3—61no—
347#239—62no—
348#239—62no—
349#237—62no—
350#237—62no—
351D3×D4—22no—
352D3×D4D1214yescomplemented
353#235—62no—
354#235—62no—
355#235—62no—
356#235—62no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—44no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3#6711yescharacteristic
373C2×C4×D3#6711yescharacteristic
374C2×C4×D3C22×D311yescharacteristic
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—61no—
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—62no—
380C3×D8—62no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—41no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—21no—
397C3×C42—31no—
398C3×C42—31no—
399C3×C42—31no—
400C3×C42C22×D311yescharacteristic
401C3×C42C22×D311yescharacteristic
402#217—21no—
403#215—62no—
404#214—22no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—122no—
410#213—22no—
411#213—62no—
412#213—62no—
413#213—62no—
414#213—62no—
415#213—62no—
416#213—122no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4—121no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433C4×Dic3#6711yescharacteristic
434C4×Dic3#6711yescharacteristic
435C4×Dic3C22×D311yescharacteristic
436#208—62no—
437#208—62no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—62no—
447#204—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—62no—
450C22×C32—22no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—48no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#12112yes—
467C32×C4—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—41no—
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3#12112yes—
477C3×Dic3AGL(1,ℤ/8)12yescomplemented
478C2×#41—91no—
479C2×#41—91no—
480C22×D4—31no—
481C23×C4—61no—
482AGL(1,ℤ/8)—184no—
483AGL(1,ℤ/8)—184no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×D8—31no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—91no—
493C2×M16—91no—
494C4⋊Q8—91no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500C4×D4—31no—
501C4×D4—31no—
502C4×D4—31no—
503C4×D4—61no—
504C4×D4—61no—
505C4×D4—181no—
506C4×D4—181no—
507C4×D4D3211yescharacteristic
508C2×C4⋊C4—31no—
509C2×C22⋊C4—61no—
510C2×C42—31no—
511C4⋊C8—31no—
512C4⋊C8—91no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515#103—31no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—31no—
526C23×C3—41no—
527C23×C3—64no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—122no—
531C23×C3—122no—
532C22×D3—21no—
533C22×D3—24no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—121no—
540C22×D3C2×#6711yescharacteristic
541C3×Q8—61no—
542C3×Q8—61no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—22no—
546C3×D4—32no—
547C3×D4—41no—
548C3×D4—64no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4C2×D1212yes—
553C3×D4D3×D412yes—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—42no—
566C2×C3×C4—42no—
567C2×C3×C4—62no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—82no—
571C2×C3×C4—121no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4—122no—
575C2×C3×C4—122no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C2×#6711yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—24no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—42no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3C2×#6711yescharacteristic
596C2×Dic3C2×#6711yescharacteristic
597C2×Dic3C2×#6711yescharacteristic
598D12—21no—
599D12—21no—
600D12—21no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—121no—
606D12—121no—
607D12—122no—
608D12—122no—
609D12—122no—
610D12C2×D1212yes—
611C4×D3—22no—
612C4×D3—41no—
613C4×D3—42no—
614C4×D3—42no—
615C4×D3—42no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—122no—
619C4×D3C2×D1212yes—
620C4×D3#23512yes—
621Dic6—21no—
622Dic6—21no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—121no—
628Dic6—121no—
629C3×C8—61no—
630C3×C8—61no—
631C3⋊C8—21no—
632C3⋊C8—21no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—121no—
638C3⋊C8—121no—
639C2×C32—42no—
640C2×C32C2×#12111yescharacteristic
641C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
642C2×C32#57511yescharacteristic
643C3⋊D3—81no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—81no—
647C24—61no—
648#41—182no—
649#41—182no—
650#41—182no—
651#41—182no—
652C2×Q8—31no—
653C2×Q8—91no—
654C2×D4—34no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—62no—
658C2×D4—61no—
659C2×D4—91no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4—181no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—21no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—124no—
674C22×C4—181no—
675C22×C4—181no—
676SD16—62no—
677SD16—182no—
678SD16—182no—
679SD16—182no—
680D8—62no—
681D8—182no—
682D8—182no—
683D8—182no—
684M16—182no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8—91no—
690C4⋊C4—31no—
691C4⋊C4—61no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4C2×D3211yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—31no—
705C42—31no—
706C42C2×D3211yescharacteristic
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—21no—
710C22×C3—32no—
711C22×C3—42no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—62no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—128no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3C2×D3×D411yescharacteristic
728C22×C3C22×#6711yescharacteristic
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—22no—
732C2×D3—48no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—241no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3#93012yes—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—32no—
755C3×C4—32no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—61no—
761C3×C4—81no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C22×D1211yescharacteristic
765C3×C4C2×#23511yescharacteristic
766C3×C4C2×D3×D411yescharacteristic
767C3×C4D3×#4111yescharacteristic
768Dic3—21no—
769Dic3—41no—
770Dic3—41no—
771Dic3—121no—
772Dic3—121no—
773Dic3—241no—
774Dic3#93012yes—
775Dic3#93212yescomplemented
776C32#303611yescharacteristic, complemented, Sylow
777C23—21no—
778C23—31no—
779C23—64no—
780C23—61no—
781C23—61no—
782C23—122no—
783C23—122no—
784C23—181no—
785Q8—61no—
786Q8—61no—
787Q8—181no—
788Q8—181no—
789D4—21no—
790D4—32no—
791D4—64no—
792D4—61no—
793D4—61no—
794D4—61no—
795D4—181no—
796D4—181no—
797D4—362no—
798D4—362no—
799D4—362no—
800D4—362no—
801D4D3×D1212yes—
802C2×C4—21no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—31no—
808C2×C4—42no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—121no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4—181no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4D3×#6711yescharacteristic
821C2×C4D3×#6711yescharacteristic
822C2×C4C22×D3211yescharacteristic
823C8—61no—
824C8—61no—
825C8—181no—
826C8—181no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—62no—
833C2×C3—82no—
834C2×C3—122no—
835C2×C3—241no—
836C2×C3D3×#12111yescharacteristic
837C2×C3#576811yescharacteristic
838C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
839C2×C3C2×#93011yescharacteristic
840C2×C3C2×#93211yescharacteristic
841C2×C3#582211yescharacteristic
842D3—22no—
843D3—42no—
844D3—81no—
845D3—241no—
846D3—241no—
847D3—481no—
848C22—22no—
849C22—32no—
850C22—41no—
851C22—41no—
852C22—61no—
853C22—61no—
854C22—62no—
855C22—128no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22C2×D3×#6711yescharacteristic
865C4—21no—
866C4—21no—
867C4—32no—
868C4—32no—
869C4—41no—
870C4—61no—
871C4—121no—
872C4—121no—
873C4—361no—
874C4C2×D3×D1211yescharacteristic
875C4D3×#23511yescharacteristic
876C3—21no—
877C3#8053411yescharacteristic, complemented
878C3#8230711yescharacteristic, complemented
879C2—42no—
880C2—62no—
881C2—122no—
882C2—241no—
883C2—721no—
884C2D3×#93011yescharacteristic
885C2D3×#93211yescharacteristic
886C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C4×D3×D4C2semidirect
2. C2×#63934C2semidirect
3. C2×#63932C2semidirect
4. #10593969C2semidirect
5. #10592715C2semidirect
6. C3×#5016C2semidirect
7. #10591489C2semidirect
8. #10591481C2semidirect
9. #10590609C2semidirect
10. #10590607C2semidirect
11. #10590559C2semidirect
12. #10590547C2semidirect
13. #10590366C2semidirect
14. #10590348C2semidirect
15. #10590336C2semidirect
25. #64084C22semidirect
34. C3×#875C22semidirect
39. #63911C22semidirect
44. #63866C22semidirect
51. #63637C22semidirect
52. #63636C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#810C22semidirect
55. C3×#809C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
69. C4×D3×D4D3semidirect
82. #5016D3semidirect
102. C3×D3×D4D4semidirect
218. #875C2×D3semidirect
239. #810C2×D3semidirect
245. #809C2×D3semidirect
251. C4⋊(C3⋊C8)C2×D3semidirect
352. D3×D4D12semidirect
477. C3×Dic3AGL(1,ℤ/8)semidirect
775. Dic3#932semidirect
776. C32#3036semidirect
877. C3#80534semidirect
878. C3#82307semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C4×D3×D42
C2×#639342
C2×#639322
#105939692
#105927152
C3×#50162
#105914892
#105914812
#105906092
#105906072
#105905592
#105905472
#105903662
#105903482
#105903362
#823073
#805343